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Navier Stokes Equations In order to use linear equation solver we need to solve two problems: 1)find velocities that constitute in advection coefficients 2) link pressure field with continuity equation This velocities that constitute advection coefficients: F=  V Pressure is in momentum equations which already has one unknown Continuity equation Momentum x Momentum y Momentum z

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Pressure and velocities in NS equations How to find velocities that constitute advection coefficients? For the first step use Initial guess And for next iterative steps use the values from previous iteration

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Pressure and velocities in NS equations How to link pressure field with continuity equation? SIMPLE ( Semi-Implicit Method for Pressure-Linked Equations ) algorithm The momentum equations can be solved only when the pressure field is given or is somehow estimated. Use * for estimated pressure and the corresponding velocities P E W xx xx xx Ae Aw Aw=Ae=A side We have two additional equations for y and x directions